A quartz crystal inside the oscillator is the resonator. It can be made of either natural or synthetic quartz, but all modern devices use synthetic quartz. The crystal strains (expands or contracts) when a voltage is applied. When the voltage is reversed, the strain is reversed. This is known as the piezoelectric effect. Oscillation is sustained by taking a voltage signal from the resonator, amplifying it, and feeding it back to the resonator. The rate of expansion and contraction is the resonance frequency and is determined by the cut and size of the crystal. The output frequency of a quartz oscillator is either the fundamental resonance or a multiple of the resonance, called an overtone frequency. Most high stability units use either the third or fifth overtone to achieve a high Q. Overtones higher than fifth are rarely used because they make it harder to tune the device to the desired frequency. A typical Q for a quartz oscillator ranges from 10 4 to 10 6 . The maximum Q for a high stability quartz oscillator can be estimated as Q = 1.6 × 10 7 /f, where f is the resonance frequency in megahertz. Environmental changes due to temperature, humidity, pressure, and vibration can change the reso- nance frequency of a quartz crystal, but there are several designs that reduce these environmental effects. The oven-controlled crystal oscillator (OCXO) encloses the crystal in a temperature-controlled chamber called an oven. When an OCXO is turned on, it goes through a ‘‘warm-up’’ period while the temperatures of the crystal resonator and its oven stabilize. During this time, the performance of the oscillator continuously changes until it reaches its normal operating temperature. The temperature within the oven then remains constant, even when the outside temperature varies. An alternate solution to the temperature problem is the temperature-compensated crystal oscillator (TCXO). In a TCXO, the signal from a temperature sensor is used to generate a correction voltage that is applied to a voltage-variable reactance, or varactor. The varactor then produces a frequency change equal and opposite to the frequency change produced by temperature. This technique does not work as well as oven control, but is less expensive. Therefore, TCXOs are used when high stability over a wide temperature range is not required. Quartz oscillators have excellent short-term stability. An OCXO might be stable ( σ y ( τ ), at τ = 1 s) to 1 × 10 -12 . The limitations in short-term stability are due mainly to noise from electronic components in the oscillator circuits. Long-term stability is limited by aging, or a change in frequency with time due to internal changes in the oscillator. Aging is usually a nearly linear change in the resonance frequency that can be either positive or negative, and occasionally, a reversal in direction of aging occurs. Aging has many possible causes including a build-up of foreign material on the crystal, changes in the oscillator circuitry, TABLE 17.5 Summary of Oscillator Types Oscillator Type Quartz (TCXO) Quartz (OCXO) Rubidium Commercial Cesium Beam Hydrogen Maser Q10 4 to 10 6 3.2 × 10 6 (5 MHz) 10 7 10 8 10 9 Resonance frequency Various Various 6.834682608 GHz 9.192631770 GHz 1.420405752 GHz Leading cause of failure None None Rubidium lamp (life expectancy >15 years) Cesium beam tube (life expectancy of 3 to 25 years) Hydrogen depletion (life expectancy >7 years) Stability, σ y ( τ ), τ = 1 s 1 × 10 -8 to 1 × 10 -9 1 × 10 -12 5 × 10 -11 to 5 × 10 -12 5 × 10 -11 to 5 × 10 -12 1 × 10 -12 Noise floor, σ y ( τ ) 1 × 10 -9 ( τ = 1 to 10 2 s) 1 × 10 -12 ( τ = 1 to 10 2 s) 1 × 10 -12 ( τ = 10 3 to 10 5 s) 1 × 10 -14 ( τ = 10 5 to 10 7 s) 1 × 10 -15 ( τ = 10 3 to 10 5 s) Aging/year 5 × 10 -7 5 × 10 -9 1 × 10 -10 None ~ 1 × 10 -13 Frequency offset after warm-up 1 × 10 -6 1 × 10 -8 to 1 × 10 -10 5 × 10 -10 to 5 × 10 -12 5 × 10 -12 to 1 × 10 -14 1 × 10 -12 to 1 × 10 -13 Warm-Up period <10 s to 1 × 10 -6 <5 min to 1 × 10 -8 <5 min to 5 × 10 -10 30 min to 5 × 10 -12 24 h to 1 × 10 -12 ©2002 CRC Press LLC A quartz crystal inside the oscillator is the resonator. It can be made of either natural or synthetic quartz, but all modern devices use synthetic quartz. The crystal strains (expands or contracts) when a voltage is applied. When the voltage is reversed, the strain is reversed. This is known as the piezoelectric effect. Oscillation is sustained by taking a voltage signal from the resonator, amplifying it, and feeding it back to the resonator. The rate of expansion and contraction is the resonance frequency and is determined by the cut and size of the crystal. The output frequency of a quartz oscillator is either the fundamental resonance or a multiple of the resonance, called an overtone frequency. Most high stability units use either the third or fifth overtone to achieve a high Q. Overtones higher than fifth are rarely used because they make it harder to tune the device to the desired frequency. A typical Q for a quartz oscillator ranges from 10 4 to 10 6 . The maximum Q for a high stability quartz oscillator can be estimated as Q = 1.6 × 10 7 /f, where f is the resonance frequency in megahertz. Environmental changes due to temperature, humidity, pressure, and vibration can change the reso- nance frequency of a quartz crystal, but there are several designs that reduce these environmental effects. The oven-controlled crystal oscillator (OCXO) encloses the crystal in a temperature-controlled chamber called an oven. When an OCXO is turned on, it goes through a ‘‘warm-up’’ period while the temperatures of the crystal resonator and its oven stabilize. During this time, the performance of the oscillator continuously changes until it reaches its normal operating temperature. The temperature within the oven then remains constant, even when the outside temperature varies. An alternate solution to the temperature problem is the temperature-compensated crystal oscillator (TCXO). In a TCXO, the signal from a temperature sensor is used to generate a correction voltage that is applied to a voltage-variable reactance, or varactor. The varactor then produces a frequency change equal and opposite to the frequency change produced by temperature. This technique does not work as well as oven control, but is less expensive. Therefore, TCXOs are used when high stability over a wide temperature range is not required. Quartz oscillators have excellent short-term stability. An OCXO might be stable ( σ y ( τ ), at τ = 1 s) to 1 × 10 -12 . The limitations in short-term stability are due mainly to noise from electronic components in the oscillator circuits. Long-term stability is limited by aging, or a change in frequency with time due to internal changes in the oscillator. Aging is usually a nearly linear change in the resonance frequency that can be either positive or negative, and occasionally, a reversal in direction of aging occurs. Aging has many possible causes including a build-up of foreign material on the crystal, changes in the oscillator circuitry, TABLE 17.5 Summary of Oscillator Types Oscillator Type Quartz (TCXO) Quartz (OCXO) Rubidium Commercial Cesium Beam Hydrogen Maser Q10 4 to 10 6 3.2 × 10 6 (5 MHz) 10 7 10 8 10 9 Resonance frequency Various Various 6.834682608 GHz 9.192631770 GHz 1.420405752 GHz Leading cause of failure None None Rubidium lamp (life expectancy >15 years) Cesium beam tube (life expectancy of 3 to 25 years) Hydrogen depletion (life expectancy >7 years) Stability, σ y ( τ ), τ = 1 s 1 × 10 -8 to 1 × 10 -9 1 × 10 -12 5 × 10 -11 to 5 × 10 -12 5 × 10 -11 to 5 × 10 -12 1 × 10 -12 Noise floor, σ y ( τ ) 1 × 10 -9 ( τ = 1 to 10 2 s) 1 × 10 -12 ( τ = 1 to 10 2 s) 1 × 10 -12 ( τ = 10 3 to 10 5 s) 1 × 10 -14 ( τ = 10 5 to 10 7 s) 1 × 10 -15 ( τ = 10 3 to 10 5 s) Aging/year 5 × 10 -7 5 × 10 -9 1 × 10 -10 None ~ 1 × 10 -13 Frequency offset after warm-up 1 × 10 -6 1 × 10 -8 to 1 × 10 -10 5 × 10 -10 to 5 × 10 -12 5 × 10 -12 to 1 × 10 -14 1 × 10 -12 to 1 × 10 -13 Warm-Up period <10 s to 1 × 10 -6 <5 min to 1 × 10 -8 <5 min to 5 × 10 -10 30 min to 5 × 10 -12 24 h to 1 × 10 -12 ©2002 CRC Press LLC 18 Sensor and Actuator Characteristics 18.1 Range 18.2 Resolution 18.3 Sensitivity 18.4 Error 18.5 Repeatability 18.6 Linearity and Accuracy 18.7 Impedance 18.8 Nonlinearities 18.9 Static and Coulomb Friction 18.10 Eccentricity 18.11 Backlash 18.12 Saturation 18.13 Deadband 18.14 System Response 18.15 First-Order System Response 18.16 Underdamped Second-Order System Response 18.17 Frequency Response Mechatronic systems use a variety of sensors and actuators to measure and manipulate mechanical, electrical, and thermal systems. Sensors have many characteristics that affect their measurement capa- bilities and their suitability for each application. Analog sensors have an output that is continuous over a finite region of inputs. Examples of analog sensors include potentiometers, LVDTs (linear variable differential transformers), load cells, and thermistors. Digital sensors have a fixed or countable number of different output values. A common digital sensor often found in mechatronic systems is the incremental encoder. An analog sensor output conditioned by an analog-to-digital converter (ADC) has the same digital output characteristics, as seen in Fig. 18.1. 18.1 Range The range (or span) of a sensor is the difference between the minimum (or most negative) and maximum inputs that will give a valid output. Range is typically specified by the manufacturer of the sensor. For example, a common type K thermocouple has a range of 800 ∞ C (from - 50 ∞ C to 750 ∞ C). A ten-turn potentiometer would have a range of 3600 degrees. Joey Parker University of Alabama ©2002 CRC Press LLC 19 Sensors 19.1 Linear and Rotational Sensors Contact • Infrared • Resistive • Tilt (Gravity) • Capacitive • AC Inductive • DC Magnetic • Ultrasonic • Magnetostrictive Time-of-Flight • Laser Interferometry 19.2 Acceleration Sensors Overview of Accelerometer Types • Dynamics and Characteristics of Accelerometers • Vibrations • Typical Error Sources and Error Modeling • Inertial Accelerometers • Electromechanical Accelerometers • Piezoelectric Accelerometers • Piezoresistive Accelerometers • Strain-Gauge Accelerometers • Electrostatic Accelerometers • Micro- and Nanoaccelerometers • Signal Conditioning and Biasing 19.3 Force Measurement General Considerations • Hooke’s Law • Force Sensors 19.4 Torque and Power Measurement Fundamental Concepts • Arrangements of Apparatus for Torque and Power Measurement • Torque Transducer Technologies • Torque Transducer Construction, Operation, and Application • Apparatus for Power Measurement 19.5 Flow Measurement Introduction • Terminology • Flow Characteristics • Flowmeter Classification • Differential Pressure Flowmeter • The Variable Area Flowmeter • The Positive Displacement Flowmeter • The Turbine Flowmeter • The Vortex Shedding Flowmeter • The Electromagnetic Flowmeter • The Ultrasonic Flowmeter • The Coriolis Flowmeter • Two-Phase Flow • Flowmeter Installation • Flowmeter Selection 19.6 Temperature Measurements Introduction • Thermometers That Rely Upon Differential Expansion Coefficients • Thermometers That Rely Upon Phase Changes • Electrical Temperature Sensors and Transducers • Noncontact Thermometers • Microscale Temperature Measurements • Closing Comments 19.7 Distance Measuring and Proximity Sensors Distance Measuring Sensors • Proximity Sensors 19.8 Light Detection, Image, and Vision Systems Introduction • Basic Radiometry • Light Sources • Light Detectors • Image Formation • Image Sensors • Vision Systems 19.9 Integrated Microsensors Introduction • Examples of Micro- and Nanosensors • Future Development Trends • Conclusions Kevin M. Lynch Northwestern University Michael A. Peshkin Northwestern University Halit Eren Curtin University of Technology M. A. Elbestawi McMaster University Ivan J. Garshelis Magnova, Inc. Richard Thorn University of Derby Pamela M. Norris University of Virginia Bouvard Hosticka University of Virginia Jorge Fernando Figueroa NASA Stennis Space Center H. R. (Bart) Everett Space and Naval Warfare Systems Center Stanley S. Ipson University of Bradford Chang Liu University of Illinois ©2002 CRC Press LLC . multiple of the resonance, called an overtone frequency. Most high stability units use either the third or fifth overtone to achieve a high Q. Overtones higher than fifth are rarely used because they make. either the fundamental resonance or a multiple of the resonance, called an overtone frequency. Most high stability units use either the third or fifth overtone to achieve a high Q. Overtones higher. to the resonator. The rate of expansion and contraction is the resonance frequency and is determined by the cut and size of the crystal. The output frequency of a quartz oscillator is either the